What in the world does it mean when a recipe says to "sweat" vegetables? Should you take them for a few laps around the kitchen? Nope...no need to run laps around your kitchen; at least, not when it comes sweating vegetables.
To "sweat" vegetables means to cook them over low to medium heat so they release some of their juices without browning (i.e. sweat!). You'll often encounter this cooking instruction when making soups, stews, or sauces - onions and other aromatic vegetables are often sweated to release more flavor.
Be sure to stir the vegetables frequently and adjust the heat to prevent browning. Also, make sure you have enough butter or oil in the pan to keep the veggies from getting dry.